Differential equations with irregular singular points in dimension two. (Équations différentielles à points singuliers irréguliers en dimension 2.) (French) Zbl 0803.32005

Sabbah, Claude

Ann. Inst. Fourier 43, No. 5, 1619-1688 (1993).

We associate a fibration with each meromorphic connection in dimension 2, which is related with the irregularity complex of the connection along its singular locus, and generalizes the notion of a Stokes line in dimension 1. This construction is made under the hypothesis that the connection has a “good formal structure” after (complex) blowing up.

Reviewer: C.Sabbah (Palaiseau)

MSC:

32C38	Sheaves of differential operators and their modules, \(D\)-modules
34M99	Ordinary differential equations in the complex domain
32S30	Deformations of complex singularities; vanishing cycles

Keywords:

real blowing up; irregularity; meromorphic connection

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